Ecological Models on Multi Species Interaction within Unlimited Resources

Abstract

In this paper, we present a three species food web system in that two species are interacting mutually and a third species, which is a predator to the first species and host for the second species i.e. there is a commensalism interaction between second and third species. All three species considered in unbounded availability of natural resources. The analytical investigations of this ecological model are observed by employing known direct methods if not by numerical methods. This model is characterized by a system of first order nonlinear ordinary coupled differential equations. We investigate three cases: (1) The death rate of any one (say third species) species is greater than its birth rate. (2) The death rates of any two species (say second, third) are greater than their birth rates. (3) The death rates of all the species are greater than their birth rates. Further the local stability at existing equilibrium points and global stability by suitable parametric values to the model equations are examined. The numerical simulations are supporting the analytical findings. As a whole we can conclude that the ecological food systems involving such kind of interactions may exist for a long time under certain environmental conditions.

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Acknowledgements

The authors are highly indebted to the referees of this paper, who helped us to improve our presentation with their remarkable comments. Also, the authors do sincerely thank Professor O.D. Makinde on adding an example for improving the content of the paper.

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All authors contributed equally to write of this paper. All authors have read and approved the final manuscript.

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Correspondence to N. Seshagiri Rao.

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Seshagiri Rao, N., Kalyani, K. Ecological Models on Multi Species Interaction within Unlimited Resources. Int. J. Appl. Comput. Math 6, 95 (2020). https://doi.org/10.1007/s40819-020-00847-w

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Keywords

  • Mutualism interaction
  • Commensalism interaction
  • Predator
  • Equilibrium points
  • Local stability
  • Global stability
  • Numerical simulations

Mathematics Subject Classification

  • 92B05
  • 92D25
  • 93A30
  • 93C15